Isocost
Encyclopedia
In economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

 an isocost line shows all combinations of inputs which cost the same total amount. Although similar to the budget constraint
Budget constraint
A budget constraint represents the combinations of goods and services that a consumer can purchase given current prices with his or her income. Consumer theory uses the concepts of a budget constraint and a preference map to analyze consumer choices...

 in consumer theory
Consumer theory
Consumer choice is a theory of microeconomics that relates preferences for consumption goods and services to consumption expenditures and ultimately to consumer demand curves. The link between personal preferences, consumption, and the demand curve is one of the most closely studied relations in...

, the use of the isocost line pertains to cost-minimization in production, as opposed to utility-maximization. For the two production inputs
Factors of production
In economics, factors of production means inputs and finished goods means output. Input determines the quantity of output i.e. output depends upon input. Input is the starting point and output is the end point of production process and such input-output relationship is called a production function...

 labour and capital, with fixed unit costs of the inputs, the equation of the isocost line is

where w represents the wage rate of labour, r represents the rental rate of capital, K is the amount of capital used, L is the amount of labour used, and C is the total cost of acquiring those quantities of the two inputs.

The absolute value of the slope of the isocost line, with capital plotted vertically and labour plotted horizontally, equals the ratio of unit costs of labour and capital. The slope is:


The isocost line is combined with the isoquant
Isoquant
In economics, an isoquant is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs...

 map to determine the optimal production point at any given level of output. Specifically, the point of tangency between any isoquant and an isocost line gives the lowest-cost combination of inputs that can produce the level of output associated with that isoquant. Equivalently, it gives the maximum level of output that can be produced for a given total cost of inputs. A line joining tangency points of isoquants and isocosts (with input prices held constant) is called the expansion path
Expansion path
In economics, an expansion path is a line connecting optimal input combinations as the scale of production expands...

.

The cost-minimization problem

The cost-minimization problem of the firm is to choose an input bundle (K,L) feasible for the output level y that costs as little as possible. A cost-minimizing input bundle is a point on the isoquant for the given y that is on the lowest possible isocost line. Put differently, a cost-minimizing input bundle must satisfy two conditions:
  1. it is on the y-isoquant
  2. no other point on the y-isoquant is on a lower isocost line.

The case of smooth isoquants convex to the origin

If the y-isoquant is smooth and convex to the origin and the cost-minimizing bundle involves a positive amount of each input, then at a cost-minimizing input bundle an isocost line is tangent to the y-isoquant.
Now since the absolute value of the slope of the isocost line is the input cost ratio , and the absolute value of the slope of an isoquant is the marginal rate of technical substitution (MRTS), we reach the following conclusion:
If the isoquants are smooth and convex to the origin and the cost-minimizing input bundle involves a positive amount of each input, then this bundle satisfies the following two conditions:
  • It is on the y-isoquant (i.e. F(K, L) = y where F is the production function
    Production function
    In microeconomics and macroeconomics, a production function is a function that specifies the output of a firm, an industry, or an entire economy for all combinations of inputs...

    ), and

  • the MRTS at (K, L) equals w/r.


The condition that the MRTS be equal to w/r can be given the following intuitive interpretation. We know that the MRTS is equal to the ratio of the marginal products of the two inputs. So the condition that the MRTS be equal to the input cost ratio is equivalent to the condition that the marginal product per dollar is equal for the two inputs. This condition makes sense: at a particular input combination, if an extra dollar spent on input 1 yields more output than an extra dollar spent on input 2, then more of input 1 should be used and less of input 2, and so that input combination cannot be optimal. Only if a dollar spent on each input is equally productive is the input bundle optimal.
The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
x
OK